Statistical theory on finite alphabet structures: inference, algorithms, and applications

有限字母表结构的统计理论：推理、算法和应用

• 批准号: 411042450
• 负责人: Dr. Merle Behr
• 金额: --
• 依托单位: Department of Statistics
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/411042450?language=en
• 关键词: Statistical; theory; finite; alphabet; structures

A vast amount of research of modern statistics is concerned with problems that are highly underdetermined, in the sense that the amount of unknown parameters is (much) larger than the amount of observable data. This renders estimation of and inference about such parameters impossible per se, as the parameters are not identifiable. Therefore, it is pertinent to include additional structural information. In a broader sense, this is achieved by some kind of sparsity: although the parameter of interest is complex (e.g., high-dimensional), it has a simple (e.g., low-dimensional) underlying structure. The focus of this proposal is on a type of sparsity that has received relatively few attention so far, namely, sparsity in the function values of a signal via a given finite alphabet (FA). FA structures appear in many different fields, for example, in cancer genetics, where DNA copy-numbers can only take one of a few known integer values, and in digital communications with binary signals.In the theoretical part of this project, we want to analyze, jointly with Prof. Martin Wainwright (UC Berkeley) and Prof. Bin Yu (UC Berkeley), how FA structures can enable meaningful inference in underdetermined statistical models, in place of and in combination with classical sparsity. Thereby, we want to focus on blind source separation and high-dimensional linear models. Although, FA structures solve the problem of non-identifiability, their combinatorial nature leads to a computational burden. Therefore, a fundamental research objective of this proposal is to precisely quantify this gap between statistical minimax optimality and computational feasibility. In particular, we want to develop fast algorithms, which, at the same time, yield adequate statical efficiency.On this basis, in the analytical part of this project, we want to consider a modification of FA structures: Subgroup detection for clinical trials often leads to segmentation problems, where a specific FA is induced by phylogenetic trees. We want to tackle those problems with multiscale procedures. Those do not just provide minimax optimal estimates, but also confidence statements, something which can be particularly crucial in medical applications. In cooperation with Prof. Bin Yu (UC Berkeley) and the Wellcome Trust Center for Human Genetics (Oxford) we want to demonstrate with real data examples how FA-procedures provide significant improvement in personalized medicine.

关于现代统计数据的大量研究与高度不确定的问题有关，因为未知参数的数量（大量）大于可观察到的数据量。这使得对此类参数的估计本身是不可能的，因为参数无法识别。因此，有必要包括其他结构信息。从广义上讲，这是通过某种稀疏性实现的：尽管感兴趣的参数是复杂的（例如，高维），但它具有简单的（例如，低维）的基础结构。该提案的重点是到目前为止吸引了相对较少注意力的一种稀疏性，即通过给定有限字母（FA）在信号的功能值中的稀疏性。 FA结构出现在许多不同的领域中，例如，在癌症遗传学中，DNA拷贝数只能采用少数已知的整数值之一，并且在与二进制信号的数字通信中。在该项目的理论部分，我们希望与Martin Wainwright教授（UC Berkeley）和Bin Yu教授（UC Berkeley）共同分析FA结构如何在不确定的统计模型中实现有意义的推断，并与经典的稀疏性相结合。 因此，我们希望专注于盲源分离和高维线性模型。尽管FA结构解决了非识别性问题，但它们的组合性质导致了计算负担。 因此，该提案的基本研究目标是精确量化统计最小值和计算可行性之间的差距。特别是，我们希望开发快速算法，同时，该算法会产生足够的静态效率。在此基础上，在本项目的分析部分中，我们想考虑对FA结构的修改：通常用于临床试验的亚组检测导致分割问题，其中特定的FA是由系统发育树诱导的。我们想通过多尺度程序解决这些问题。这些不仅提供了最小值的最佳估计，还提供信心陈述，这在医疗应用中可能特别至关重要。与Bin Yu教授（UC Berkeley）和Wellcome人类遗传学中心（牛津）合作，我们希望通过真实的数据示例来证明FA-Procedures如何为个性化医学提供显着改善。

项目成果

Multiple haplotype reconstruction from allele frequency data

• DOI: 10.1038/s43588-021-00056-5
• 发表时间: 2021-04-01
• 期刊: NATURE COMPUTATIONAL SCIENCE
• 作者: Pelizzola, Marta;Behr, Merle;Futschik, Andreas
• 通讯作者: Futschik, Andreas

Testing for dependence on tree structures

• DOI: 10.1073/pnas.1912957117
• 发表时间: 2020-05-05
• 期刊: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• 影响因子: 11.1
• 作者: Behr, Merle;Ansari, M. Azim;Holmes, Chris
• 通讯作者: Holmes, Chris